Coupled Electromagnetic Field/Circuit Simulation. Modeling and Numerical Analysis
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Beschreibung
Today's most commonly used circuit models increasingly tend to lose their validity in circuit simulation due to rapid technological developments,
miniaturization and increased complexity of integrated circuits. The starting
point of this thesis was to tackle these challenges by refining the critical
parts of the circuit by combining circuit simulation directly with distributed
device models.
The approach set out in this thesis couples partial differential equations for
electromagnetic devices - modeled by Maxwell's equations -, to
differential-algebraic equations, which describe basic circuit elements
including memristors and the circuit's topology.
First, Maxwell's equations are spatially discretized and a potential formulation
is derived, the coupled system is then formulated as a differential-algebraic
equation with a properly stated leading term and analyzed. Topological and
modeling conditions are presented to guarantee the tractability index of these
differential-algebraic equations to be no greater than two.
Finally, local solvability, perturbation results and an algorithm to calculate
consistent initializations are derived for a general class of
differential-algebraic equations with a properly stated leading term having
tractability index-2.
Autor*in
Sascha Baumanns
Themen in »Coupled Electromagnetic Field/Circuit Simulation. Modeling and Numerical Analysis«
differential-algebraic equation tractability index Maxwell's equation circuit simulation finite integration technique